Page 136 - MATLAB Recipes for Earth Sciences

130 6 Signal Processing

Input signal x(t)
bi T
Output signal y(t)

+ +

T ai

Fig. 6.2 Schematic of a linear time-invariant fi lter with an input x(t) and an output y(t). The

filter is characterized by its weights a and b , and the delay elements T. Nonrecursive fi lters
i i
only have nonrecursive weights b , whereas the recursive filter also requires the recursive

i
fi lters weights a .
i

with the known problems in the design of zero-phase filters. The larger of
the two quantities M and N +N or N, respectively, is the order of the fi lter.
1 2
We use the same synthetic input signal as in the previous example to il-
lustrate the performance of a recursive fi lter.

clear
t = (1:100)';
randn('seed',0);
x5 = randn(100,1);
We filter this input using a recursive filter with a set of weights a5 and b5,

b5 = [0.0048 0.0193 0.0289 0.0193 0.0048];
a5 = [1.0000 -2.3695 2.3140 -1.0547 0.1874];
m5 = length(b5);

y5 = filter(b5,a5,x5);
and correct the output for the phase

y5= y5(1+(m5-1)/2:end-(m5-1)/2,1);
y5(end+1:end+m5-1,1)=zeros(m5-1,1);

Now we plot the results.
plot(t,x5,'b-',t,y5,'r-')